Find the inverse function of the function f, of, x, equals, one fifth, x, plus, 5f(x)=

Question

5
1
​
x+5.
Answer
Attempt 1 out of 2
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, x, minus, 5f
−1
(x)=5x−5
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, x, minus, 25f
−1
(x)=5x−25
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, one fifth, x, minus, 25f
−1
(x)=
5
1
​
x−25
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, one fifth, x, minus, 5f
−1
(x)=
5
1
​
x−5

Answer 1

To find the inverse function of \( f(x) = \frac{1}{5}x + 5 \), we will follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = \frac{1}{5}x + 5 \]

2. Swap \( x \) and \( y \): \[ x = \frac{1}{5}y + 5 \]

3. Solve for \( y \):

   • First, isolate the term with \( y \). \[ x - 5 = \frac{1}{5}y \]
   • Now, multiply both sides by 5 to get rid of the fraction: \[ 5(x - 5) = y \]
   • Simplify: \[ y = 5x - 25 \]

4. Write the inverse function: \[ f^{-1}(x) = 5x - 25 \]

Thus, the correct answer from the provided options is: \[ f^{-1}(x) = 5x - 25 \]